The 12-lead ECG is the primary diagnostic tool in clinical cardiology. A measure of the heart’s electrical activity, characteristic changes in the morphology of 12-lead ECGs can be used to identify a wide range of cardiac conditions. As part of the PhysioNet Challenge 2020, we present an automated algorithm for the simultaneous classification of several common cardiac conditions including atrial fibrillation, first degree AV block, bundle branch block, premature complexes, and changes in the ST segment found during myocardial ischaemia. Our algorithm has been developed with a strong focus on explainability, ensuring that our classifications can be directly related to features of the 12-lead ECG that may be of relevance to a clinician. To achieve this, our classification algorithm uses an XGBoost decision tree classifier. The classification features include simple statistical properties of key ECG segments used clinically (QRS complex, PR interval etc.), combined with a number of information theoretic measures to assess the complexity of ECG signals. In particular, we study the Lempel-Ziv complexity of the ECG which assesses the compressibility of the signal. This approach has been particularly successful for classifying various neurological disorders and states of consciousness in high frequency M/EEG data. We also consider the Mutual Information and its multivariate extensions to estimate higher order dependencies among different anatomical regions of the heart (Inferior, Lateral, Septal and Anterior). Leveraging these measures, our preliminary algorithm results in a cross-validated F2 (G2) score of 0.73 (0.47) on the training data, and an F2 (G2) score of 0.69 (0.44) on unseen test data.